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Modified Newton solver for yield stress fluids. (English) Zbl 1387.76058
Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 481-490 (2016).
Summary: The aim of this contribution is to present a new Newton-type solver for yield stress fluids, for instance for viscoplastic Bingham fluids. In contrast to standard globally defined (‘outer’) damping strategies, we apply weighting strategies for the different parts inside of the resulting Jacobian matrices (after discretizing with FEM), taking into account the special properties of the partial operators which arise due to the differentiation of the corresponding nonlinear viscosity function. Moreover, we shortly discuss the corresponding extension to fluids with a pressure-dependent yield stress which are quite common for modelling granular material. From a numerical point of view, the presented method can be seen as a generalized Newton approach for non-smooth problems.
For the entire collection see [Zbl 1358.65003].

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
76A10 Viscoelastic fluids
Software:
FEATFLOW
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References:
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